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Renormalization group evaluation of exponents in family name distributions

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  • De Luca, Andrea
  • Rossi, Paolo

Abstract

According to many phenomenological and theoretical studies the distribution of family name frequencies in a population can be asymptotically described by a power law. We show that the Galton–Watson process corresponding to the dynamics of a growing population can be represented in Hilbert space, and its time evolution may be analyzed by renormalization group techniques, thus explaining the origin of the power law and establishing the connection between its exponent and the ratio between the population growth and the name production rates.

Suggested Citation

  • De Luca, Andrea & Rossi, Paolo, 2009. "Renormalization group evaluation of exponents in family name distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3609-3614.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:17:p:3609-3614
    DOI: 10.1016/j.physa.2009.04.017
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    References listed on IDEAS

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    1. Miyazima, Sasuke & Lee, Youngki & Nagamine, Tomomasa & Miyajima, Hiroaki, 2000. "Power-law distribution of family names in Japanese societies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 282-288.
    2. Panaretos, John, 1989. "On the Evolution of Surnames," MPRA Paper 6255, University Library of Munich, Germany.
    3. Kim, Beom Jun & Park, Sung Min, 2005. "Distribution of Korean family names," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 347(C), pages 683-694.
    4. Reed, William J. & Hughes, Barry D., 2003. "On the distribution of family names," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 579-590.
    5. Zanette, Damián H & Manrubia, Susanna C, 2001. "Vertical transmission of culture and the distribution of family names," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 1-8.
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